Geomechanical model for fracture deformation under hydraulic, mechanical and thermal loads

Hydraulic flow and transport (heat and solute) within crystalline rocks is dominated by the fracture systems found within them. In situ stress conditions have a significant impact on the hydraulic, mechanical and thermal coupled processes, and quantification of these processes provides a key to understanding the often transient time-dependent behaviour of crystalline rocks. In this paper, a geomechanical model is presented which describes fracture closure as a function of effective stress and the changes in parameters such as storage, permeability, porosity and aperture. Allowing the fracture closure to be defined by the change in normal effective stress provides a link to the numerical consideration of parametrical changes due to rock stress alterations caused for example by changes in fracture fluid pressure, stress release, tectonic stress, thermal stress, orientation of the natural fracture in the pervasive stress system and local changes in a rock mass due to stress alteration. The model uses geometrical considerations based on a fractal distribution of apertures on the fracture surface, and applies well-established analytical elastic deformation solutions to calculate the deformation response to changes in effective stress. Analysis of the fractal generation method allows a standard normal distribution of fracture apertures to be predicted for all common fractal dimensions relating to a 2D surface. Changes in the fracture aperture are related to hydraulic functions such as permeability, storage and porosity of the fracture. The geomechanical model is experimentally validated against laboratory scale experimental data gained from the closure of a fractured sample recovered at a depth of 3,800 m from the KTB pilot borehole. Parameters for matching the experimental data were established externally, the only fitting parameters applied were the minimum and maximum contact area between the surfaces and the number of allowable contacts. The model provides an insight into the key processes determining the closure of a fracture, and can act as a material input function for numerical models linking the effects of changes in the stress field, hydraulic or thermal conditions, to the flow and transport parameters of a fractured system.

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Résumé L’écoulement et le transport (chaleur et soluté) dans les roches cristallines sont dominés par les systèmes de fracture. Les conditions de stress in-situ ont un impact significatif sur l’hydraulique, les processus couplés de mécanique et thermique et la quantification de ces processus apportent une clé pour comprendre le comportement transitoire des roches cristallines. Dans cet article un modèle géomécanique est présenté, modèle qui décrit la fermeture des fractures comme une fonction de la contrainte effective et des changements de paramètres tels le coefficient d’emmagasinement, la perméabilité, la porosité et l’ouverture. En s’accordant que la fermeture des fractures est définit par les changements de la contrainte effective normale, on apporte le lien avec la considération numérique des changements paramétriques dus aux altérations de la contrainte des roches, causés par exemple par des variations de la pression des fluides dans les fractures, du dégagement de la contrainte, des contraintes tectoniques et thermiques, des orientations des fractures naturelles dans le système de contraintes pénétrantes, et des changements locaux dans un massif de roches dus à l’altération des contraintes. Le modèle utilise des considérations géométriques basées sur une distribution fractale des ouvertures à la surface des fractures, et permet d’établir des solutions analytiques de la déformation élastique pour calculer la réponse de la déformation à la contrainte effective. L’analyse de la méthode par génération fractale permet de prédire une distribution normale standard de l’ouverture des fractures, pour toutes les dimensions fractales en relation avec les surfaces 2D. Les changements dans l’ouverture des fractures sont mis en relation avec les fonctions hydrauliques tels la perméabilité, l’emmagasinement et la porosité de la fracture. Le modèle géoméchanique est expérimentalement validé à l’échelle du laboratoire sur un échantillon fracturé récupéré à une profondeur de 3,800 mètres sur le puits du site pilote KTB. Les paramètres du calibrage des données expérimentales ont été établies extérieurement, les seuls paramètres utilisés étant les surfaces de contact minimum et maximum, et le nombre de contacts permis. Le modèle apporte une connaissance perspicace sur le processus clé déterminant la fermeture des fractures, et peut servir de fonction input dans les modèles numériques reliant les effets des variations de la contrainte du terrain, les conditions hydrauliques ou thermales, les paramètres de l’écoulement et du transport et les systèmes de fracture.

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Resumen El flujo hidráulico y transporte (de calor y solutos) dentro de rocas cristalinas está dominado por los sistemas de fracturas que se encuentran en ellas. Las condiciones de esfuerzos in-situ tienen un impacto significativo en los procesos aparejados termales, mecánicos e hidráulicos y la cuantificación de estos procesos aporta una clave para entender el frecuente comportamiento transitorio dependiente de las rocas cristalinas. En este artículo se presenta un modelo geomecánico que describe el cierre de fracturas en función del esfuerzo efectivo y los cambios en parámetros tal como almacenamiento, permeabilidad, porosidad y apertura. El definir el cierre de fractura mediante el cambio en esfuerzo normal efectivo aporta un vínculo con la consideración numérica de cambios paramétricos ocasionados por alteraciones de esfuerzos en la roca causadas, por ejemplo, por cambios en presión de fluidos en fractura, liberación de esfuerzo, esfuerzo tectónico, esfuerzo termal, orientación de fracturas naturales en el sistema de esfuerzos penetrante, y cambios locales en una masa rocosa ocasionados por alteración de esfuerzos. El modelo utiliza consideraciones geométricas basadas en la distribución fractal de aperturas en la superficie de fractura y aplica soluciones analíticas bien establecidas de deformación elástica para calcular la respuesta de deformación a cambios en el esfuerzo efectivo. Los análisis del método de generación fractal permiten predecir una distribución normal standard para la distribución de aperturas de fracturas para todas las dimensiones fractales comunes que se relacionan con una superficie 2D. Los cambios en la apertura de fractura se relacionan con funciones hidráulicas tal como permeabilidad, almacenamiento y porosidad de la fractura. El modelo geomecánico se ha validado experimentalmente en contra de datos experimentales a escala de laboratorio obtenidos a partir del cierre de una muestra fracturada recuperada a una profundidad de 3,800 m en el pozo piloto KTB. Se establecieron externamente parámetros que se ajustan a los datos experimentales, con los parámetros de ajuste aplicados que fueron el área máxima y mínima de contacto entre las superficies y el número de contactos permisibles. El modelo arroja luz sobre los procesos clave que determinan el cierre de una fractura y puede actuar como un material de función de entrada para modelos numéricos que vinculan los efectos de cambios en el campo de esfuerzos, condiciones termales o hidráulicas, con los parámetros de flujo y transporte de un sistema fracturado.

     

Fractal analysis of mingled/mixed magmas: an example from the Upper Pollara eruption (Salina Island, southern Tyrrhenian Sea, Italy)

Upper Pollara eruption products (13 ka, Salina Island, Italy) include both homogeneous and heterogeneous pumices resulting from mixing/mingling processes between an HK andesite and a high-SiO₂ rhyolite. Representative samples of heterogeneous pumices are collected and analyzed in order to check the correspondence between glass composition and morphological features of the mingling/mixing structures. Image analysis techniques are applied and eight grey color ranges (classes) are extracted from high-resolution scans of pumice. Class 1 (lighter colors) and class 8 (darker colors) show end-member glass compositions, i.e. HK andesite and high-SiO₂ rhyolite, respectively. These two classes show spot- to cluster-like morphological structures. Intermediate classes show an HK dacitic to rhyolitic composition and a banding- to fold-like morphology. Fractal analysis by box-counting of the boundary pattern of eight grey classified images is performed over a length scale of 0.028–1.8 cm. Fractal dimension D is between 1.01 and 1.84. Coupled fractal analysis and geochemical data reveal that D increases as the degree of magma interaction (homogenization) increases. This feature well fits the results from numerical models on the convective mixing of fluids driven by thermal convection. We conclude that the increase of D observed in the Upper Pollara samples reflects the transition from fractal mixing to homogenization. End-member magmas (HK andesite and high-SiO₂ rhyolite) represent isolated mixing regions, while homogenized magmas represent active mixing regions. In the analyzed pumices, isolated and active mixing regions coexist at scales between 10⁻⁴ and 10⁻² m. Morphological and compositional features of the Upper Pollara pumices result from turbulence.     

Validation of a fish farm waste resuspension model by use of a particulate tracer discharged from a point source in a coastal environment

To validate a resuspension model of particulate material (salmonid farm wastes), a UV fluorescent particle tracer was selected with similar settling characteristics. Tracer was introduced to the seabed (water depth ≈30 m) and sediment samples taken on days 0, 3, 10, 17 and 30 to measure the horizontal and vertical distribution of tracer in sediments. A concentric sampling grid was established at radii of 25, 50, 100, 150, 200, 400, 700 and 1, 000 m from the source on transects 30° apart. The bulk of the deployed tracer was initially concentrated in an area 25 m radius from the release point; tracer was observed to steadily decrease to zero over a period of 30 days. In a 200 m region measured from the release point in the direction of the residual current, the redeposition of tracer was low. A Lagrangian particle tracking model was validated using these observed data by varying resuspension model parameters within limits to obtain the best agreement between spatial and temporal distributions. The validated model generally gave good predictions of total mass budgets (±7% of total tracer released), particulary where tracer concentrations were high near the release point. Best fit model parameters (critical erosion shear stress=0.018 N m⁻², erodibility constan=60 g m⁻² d⁻¹) are at the low end of reported parameters for coastal resuspension models. Such a low critical erosion shear stress indicates that the frequency of resuspension and deposition events for freshly deposited material is high.     

δO of carbonate, quartz and phosphate from belemnite guards: implications for the isotopic record of old fossils and the isotopic composition of ancient seawater

Belemnite guards of Cretaceous and Jurassic age were found to contain varying amounts of quartz deposited both on the external surface and inside the rostrum. The oxygen isotopic composition of coexisting carbonate, quartz and phosphate from the same rostrum was measured according to well-established techniques. None of these compounds showed isotopic values in equilibrium with one another. Assuming δ¹⁸O values of the diagenetic water within the range of meteoric waters, the δ¹⁸O(SiO₂) yield temperatures in agreement with the apparent secondary origin of this phase. The δ¹⁸O(CO₃²⁻) range, with a certain continuity, between −10.8 and +0.97 PDB-1 with most of the intermediate values being within the range of the carbonate isotopic values of Mesozoic fossils. The most positive isotopic results obtained from phosphate are close to +23/+24‰ (V-SMOW). They can hardly be related to a secondary origin of the phosphate, or to the presence of diagenetic effects, since these results are among the most positive ever measured on phosphate. As far as we know there is no widespread diagenetic process determining an ¹⁸O enrichment of phosphate. The very low concentration of phosphate did not allow the determination of its mineralogical composition. All the available δ¹⁸O(PO₄³⁻) values from belemnite and non-belemnite fossils of marine origin of Tertiary and Mesozoic age are reported along with the newly measured belemnites. The following conclusions may be drawn from the data reported: (1) the pristine oxygen isotope composition of fossil marine organisms (either carbonate or phosphate) may easily undergo fairly large changes because of oxygen isotope exchange processes with diagenetic water; this process is apparent even in the case of geologically recent fossils; (2) the δ¹⁸O(PO₄³⁻) of belemnite rostra seems to be, at least in the case of the most positive results, in isotopic equilibrium with environmental water because of the similarity between the results from Cretaceous belemnites and the results from Cretaceous and Lower Tertiary pelecypods and fish teeth; 3) if so, the only feasible interpretation that can be suggested for the ¹⁸O enriched data is the possibility of a relatively large variation of the oxygen isotopic composition of ocean paleowater from Jurassic to recent time.     

Employment and Socio-spatial Relations in Australia's Cultural Economy

This paper examines the significance and contribution of Australian 'creative' industry activities in light of recent debates on the emergence of the 'cultural economy of cities'. First, census employment data and business location counts are used to illustrate patterns of metropolitan primacy and concentration in the cultural industries both across states and in Sydney. Second, the specificities of the locations of cultural production, and the links between cultural industry activities and wider urban-regional change are explored in more detail. A set of observations of urban-regional change is used to demonstrate how the notion of 'cultural economy' should include complex interactions between the material activities of consumers and producers, and the discursive worlds of image makers and place marketers. Urban renewal, housing market pressures and intra-regional migration all mediate Australian experiences of the 'cultural economy'. Such interactions, in addition to key quantitative data on employment and business activity, suggest important policy considerations.     

The BEAM-project: prediction and assessment of mixture toxicities in the aquatic environment

Freshwater and marine ecosystems are exposed to various multi-component mixtures of pollutants. Nevertheless, most ecotoxicological research and chemicals regulation focus on hazard and exposure assessment of individual substances only, the problem of chemical mixtures in the environment is ignored to a large extent. In contrast, the assessment of combination effects has a long tradition in pharmacology, where mixtures of chemicals are specifically designed to develop new products, e.g. human and veterinary drugs or agricultural and non-agricultural pesticides. In this area, two concepts are frequently used and are thought to describe fundamental relationships between single substance and mixture effects: Independent Action (Response Addition) and Concentration Addition. The question, to what extent these concepts may also be applied in an ecotoxicological and regulatory context may be considered a research topic of major importance, as the concepts would allow to make use of already existing single substance toxicity data for the predictive assessment of mixture toxicities. Two critical knowledge gaps are identified: (a) There is a lack of environmental realism, as a huge part of our current knowledge about the applicability of the concepts is restricted to artificial situations with respect to mixture composition or biological effect assessment. (b) The knowledge on what exactly is needed for using the concepts as tools for the predictive mixture toxicity assessment is insufficient. Both gaps seriously hamper the necessary, scientifically sound consideration of mixture toxicities in a regulatory context.In this paper, the two concepts will be briefly introduced, the necessity of considering the toxicities of chemical mixtures in the environment will be demonstrated and the applicability of Independent Action and Concentration Addition as tools for the prediction and assessment of mixture toxicities will be discussed. An overview of the specific aims and approaches of the BEAM project to fill in the identified knowledge gaps is given and first results are outlined.     

Onshore and offshore seismic and lithostratigraphic analysis of a deeply incised Quaternary buried valley system in the Northern Netherlands

High-resolution seismic data (onshore and offshore), geophysical borehole data as well as detailed lithofacies from airlift boreholes were acquired in northern Netherlands on and around the island of Ameland. Marine and land seismic data combined with information from land boreholes have been explored with the objective of providing a sedimentary model. Qualitative seismic facies analysis of the valley fill commonly shows a thin unit with high amplitude reflectors at the base. Thick units of variable seismic facies (transparent to high amplitude) occur higher up in the sequence. Onlap is common at mid–upper levels within the sandy valley fill (with clay in mm layering), and a transparent seismic facies, corresponding to firm clays, is common at the top. Almost all lithological unit boundaries recognised within core parameters correspond with seismic unconformities within error margins. Subunits contain multiple cyclical trends in gamma ray and grain size. Cyclical trends show lower order fluctuations in gamma radiation on a scale of less than 1 m. Gamma-ray pattern variability between units, e.g. in general coarsening-up or fining-up units, suggests migration of subaqueous outwash fans or ice margin fluctuations. Seismic results could support a headward excavation and backfilling process suggested by Praeg [Morphology, stratigraphy and genesis of buried Elsterian tunnel valleys in the southern North Sea basin [PhD thesis]: University of Edinburgh, 207 pp.; Journal of Applied Geophysics, (this volume)] as being responsible for the formation of buried valleys. On a lithological scale, a more complicated, detailed and cyclical pattern arises. Catastrophic processes are considered unlikely as being responsible for the infill sequence because of the observed small-scale facies variability and because of the presence of diamicton layers. Diamicton layers at the base of basal unconformities as well as higher in sequence could suggest subglacial deformation by grounded ice before and during the valley-fill process.     

A rooftop tuned mass damper frame

This article documents the analytical study and feasibility of placing a tuned mass damper in the form of a limber rooftop moment frame atop relatively stiff structures to reduce seismic acceleration response. Six existing structures were analytically studied using a suite of time history and response spectra records. The analyses indicate that adding mass in conjunction with a limber frame results in an increase in the fundamental period of each structure. The fundamental period increase generally results in a decrease in seismic acceleration response for the same time history and response spectra records. Owing to the limber nature of the rooftop frames, non‐linear analysis methods were required to evaluate the stability of the rooftop tuned mass damper frame. The results indicate the addition of a rooftop tuned mass damper frame reduces the seismic acceleration response for most cases although acceleration response can increase if the rooftop frame is not tuned to accommodate the specific structure's dynamic behaviour and localized soil conditions. Appropriate design of the rooftop tuned mass damper frame can result in decreased seismic acceleration response. This translates to safer structures if used as a retrofit measure or a more economical design if used for new construction. Copyright © 2003 John Wiley & Sons, Ltd.